Pass-Through Rates and the Price Effects of Mergers - Vanderbilt ...

Pass-Through Rates and the
Price Effects of Mergers
Luke Froeb ∗ and Steven Tschantz †
Vanderbilt University
Nashville, TN 37203
Gregory J. Werden ‡
U.S. Department of Justice
Washington, DC 20530
October 6, 2003
Abstract
We investigate the relationship in Bertrand oligopoly between the
price effects of mergers absent synergies and the rates at which merger
synergies are passed through to consumers in the form of lower prices.
We find that the demand conditions that cause a merger to result in
large price increases absent synergies also cause the pass-through rate
to be high. The low estimated pass-through rate and the relatively
large predicted merger effect, thus, likely were inconsistent in an important
US merger case.
JEL Classification: D43 - Oligopoly; L41 - Horizontal Anticompetitive
Practices
Keywords: pass-through; merger; efficiencies; antitrust
∗ Owen Graduate School of Management, luke.froeb@vanderbilt.edu, corresponding author.
After this paper was completed, Froeb was named Director of the Bureau of Economics,
Federal Trade Commission. The views expressed here are those of the authors
and not those of the FTC or its commissioners.
† Department of Mathematics, tschantz@math.vanderbilt.edu
‡ gregory.werden@usdoj.gov. The views expressed in this paper are not purported to
represent those of the U.S. Department of Justice.

1 Introduction
In static Bertrand oligopoly, we investigate the link between price increases
from mergers absent synergies and the pass through to consumers of marginal
cost changes associated with merger synergies. Our investigation is motivated
by US court decisions, and enforcement policies in other jurisdictions,
holding that synergies are relevant to the legality of a merger only to the extent
that they are passed on to consumers in the form of lower prices. In the
Staples–Office Depot merger case, for example, the court cited low estimated
pass-through rates as an important reason that the claimed efficiencies did
not outweigh the anticompetitive effects of the merger.
We apply the term “merger effects” to the prices increases from a merger
and model them as the difference between the non-cooperative equilibrium
in which the merged products are priced independently, and the noncooperative
equilibrium in which they are priced jointly. In our terminology,
“net” merger effects include impacts of synergies on prices, while “gross”
merger effects do not. Differences between net and gross merger effects are
the “pass-through effects” of merger synergies. They are modelled as the
difference between the post-merger equilibrium without synergies and the
post-merger equilibrium with them.
We derive expressions for the net and gross merger effects by applying
the first step in Newton’s method at the pre-merger prices. This provides
an estimator of merger effects using only information potentially available
in the observed pre-merger equilibrium. Examination of this estimator indicates
that gross merger effects and pass-through effects are closely related.
Both are determined largely by the degree of profit (demand) concavity. In
particular, holding first derivatives (e.g., demand elasticities) constant, sec-
1

ond derivatives (i.e., demand concavity) determine both gross merger effects
and pass-through.
In the context of two major US merger cases, we demonstrate the practical
importance of the association of high pass-through rates with large
merger effects. The proposed WorldCom-Sprint merger illustrates that both
pass-through and gross merger effects vary greatly with differing assumptions
about the form of demand. The proposed Staples–Office Depot merger
illustrates that price increase predictions and pass through predictions each
offer a check on the other. We find a likely inconsistency in the estimates
made the experts testifying for the Federal Trade Commission.
2 Merger Effects with Assumed Demand Forms
2.1 Merger Effects in Bertrand Industries
Consumers demand quantities given by the vector q = {q i } as a function
of the price vector p = {p i }, i = 1, . . . , n. Product i is supplied at cost c i
which is a function of just q i . Profit from this product is
π i = p i q i − c i . (1)
These n products are the merging products and all competing products with
prices that react to changes in the prices of the merging products.
If each product is controlled by a different firm, maximizing the profit
from just its product, the n first-order conditions for a Nash equilibrium are
0 = ∂π i
∂p i
= q i + (p i − mc i ) ∂q i
∂p i
, (2)
where
mc i = dc i
dq i
(3)
2

is the marginal cost of product i. We do not assume that marginal costs are
constant, although this is often done in applied work. The effect of p j on q i ,
with other prices held constant, is usually expressed in terms of elasticities:
ɛ ij = p j
q i
∂q i
∂p j
. (4)
The first-order conditions imply the familiar relation between price-cost margins
and own-price demand elasticities:
p i − mc i
p i
= − 1
ɛ ii
. (5)
When several products are controlled by the same firm, the demand
interactions among its jointly owned products are internalized. If a single
firm controls products 1 and 2, its first-order conditions are
and
0 = ∂(π 1 + π 2 )
∂p 1
= q 1 + (p 1 − mc 1 ) ∂q 1
∂p 1
+ (p 2 − mc 2 ) ∂q 2
∂p 1
(6)
0 = ∂(π 1 + π 2 )
∂p 2
= q 2 + (p 1 − mc 1 ) ∂q 1
∂p 2
+ (p 2 − mc 2 ) ∂q 2
∂p 2
. (7)
These conditions lead to different equilibrium pricing than equation 2. In
terms of the US Horizontal Merger Guidelines (1992), the difference between
these two equilibria is the “unilateral” effect of the merger between sellers
of products 1 and 2 in Bertrand oligopoly.
2.2 Predicting Gross Merger Effects
To predict the gross merger effects from differentiated products mergers,
economists commonly assume a particular functional form for demand and
estimate demand elasticities. Marginal costs are recovered from the firstorder
conditions at the pre-merger equilibrium (e.g., equation 5), and the
gross merger effects are computed by solving the post-merger first-order conditions
(e.g., equations 6 and 7), assuming the same or a different functional
3

form for demand as that used to estimate the demand elasticities.
The
foregoing process, termed “merger simulation,” is described by Werden and
Froeb (1996) and Crooke et al. (1999). Nevo (2000), Hausman et al. (1994),
Hausman and Leonard (1997), and Werden (2000) apply the technique to
particular mergers.
The simplest form of merger simulation employs a constant-elasticity approximation
to an unknown demand curve (e.g., Shapiro, 1996). Using an
estimate of the elasticity matrix at the pre-merger equilibrium, it is straightforward
to compute post-merger prices. The constant-elasticity specification
makes it unnecessary to have any information about non-merging products,
as their prices do not change in response to the merger. However, if demand
becomes more elastic as price increases, Crooke et al. (1999) show
this approach can dramatically over-estimate merger effects.
P
22
20
200%
18
16
14
100%
12
10
50%
25%
20 40 60 80 100
Q
Figure 1: Four Constant-Pass-Through-Rate Demand Curves Plotted between
the Competitive and Monopoly Prices
4

Figure 1 illustrates why an erroneous assumption as to the functional
form of demand can lead to a very large prediction error.
It plots four
demand curves for a single-product industry, all defined by the functions
⎧
⎪⎨ (a − bp) θ/(1−θ) θ < 1
q(p) = a exp(−bp) θ = 1
⎪⎩
(a + bp) θ/(1−θ) θ > 1.
These demand curves exhibit a constant pass-through rate, θ = ∂p/∂∆mc,
where ∆mc is change in marginal cost resulting from merger synergies. By
construction, the four demand curves share the same price, quantity, and
elasticity (−2) at a single point, which we make the competitive equilibrium
by assuming a constant marginal cost equal to that price. Figure 1 plots
these demand curves between the common competitive equilibrium the four
different monopoly equilibria. The differing concavities of the four demand
curves result in substantially different monopoly prices. The top demand
curve, associated with a 200% pass-through rate, yields a price–marginal cost
margin at the monopoly price nearly ten times the margin with the bottom
demand curve, associated with a 25% pass-through rate. To foreshadow the
main result of the paper, demand concavity associated with higher monopoly
prices is also associated with higher pass-through rates.
2.3 Newton’s Method for Computing
Post-Merger Equilibrium
To compute equilibrium in industries with various ownership structures, we
imagine that the pricing of each product is controlled by a single agent
that may share in the profits of other products. This heuristic allows us to
characterize different kinds of equilibria, including a pre-merger equilibrium
in which all prices are set independently, and a post-merger equilibrium in
which the merged firm maximizes the sum of profits on its jointly owned
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products.
To make this notion precise, we construct the “ownership-structure matrix,”
W = {w ij }, with w ij indicating the share of profits from product j
received by agent i setting the price of product i. Agent i thus maximizes
Ω i = ∑ j
w ij π j . (8)
The pre-merger ownership structure, for example, may have W equal to the
identity matrix, while a post-merger ownership structure may have W equal
to the identity matrix except for two off-diagonal entries. Both structures
are represented by the matrix
⎛
1 r
⎞
0
W = ⎝ r 1 0 ⎠ . (9)
0 0 1
Setting r = 0 reflects the pre-merger structure, while setting r = 1 reflects
the post-merger structure. The formulation of the model in terms of the W
matrix also can be used to incorporate partial ownership before or after a
merger, as analyzed by O’Brien and Salop (2000).
In this general formulation, the n first-order conditions are
0 = ∂Ω i
∂p i
= ∑ j
w ij
∂π j
∂p i
= w ii q i + ∑ j
w ij (p j − mc j ) ∂q j
∂p i
. (10)
These first-order conditions apply both pre- and post-merger, using the relevant
pre- and post-merger values for the w ij and mc j .
To develop an expression for the net merger effect, we review how one
uses Newton’s method to find a Nash equilibrium satisfying these first-order
conditions. Let z i = ∂Ω i /∂p i , and let z = {z i } be the vector of these
derivatives expressed as functions of p. To solve for simultaneous zeros of z,
we take an initial estimate p (0) and successively refine the estimate by the
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p (1) , p (2) , p (3) , . . . , generated by the rule
p (k+1) = p (k) − A −1 z (k) , (11)
where z (k)
A = {a ij },
= z(p (k) ) is the value of z at the latest approximation, and
a ij = ∂z i
∂p j
= w ii
∂q i
∂p j
+ w ij
∂q j
∂p i
+ ∑ k
w ik (p k − mc k ) ∂2 q k
∂p j ∂p i
, (12)
is also evaluated at p (k) . The A matrix, which indicates the slopes of the
derivatives of the profit functions, also may be written
A = ∂z
∂p . (13)
For notational simplicity, we suppress the fact that A is a function of prices
and is affected by merger through both W and the marginal costs.
Newton’s method takes a first-order approximation to z at p (k) ,
z ≈ z (k) + ∂z (
p − p (k)) , (14)
∂p
and finds the value of p that sets this approximation equal to zero. To apply
Newton’s method, it is necessary to specify an initial solution p (0) , and
the natural choice in merger analysis is the pre-merger equilibrium. Taking
z (0) to be the first-order conditions evaluated with the post-merger ownership
matrix at the pre-merger equilibrium prices, the first step in applying
Newton’s method is
p (1) = p (0) − A −1 z (0) . (15)
Solving equation 15 requires evaluation of the second derivatives of q, as
they appear in A. These second derivatives determine the sharpness of the
peaks in the merged firm’s profit function or, put another way, how much a
small deviation from optimal pricing reduces profits.
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Equation 15 is a closed-form predictor of the net merger effects using only
information potentially available at the observed pre-merger equilibrium. If
nothing is known about the functional form of demand function, equation
15 offers the best possible predictor of merger effects. If the post-merger
first-order conditions are evaluated at the pre-merger marginal costs, i.e.,
z (0) | mc pre, equation 15 yields the gross merger effect:
∆p gme = −A −1 ( z (0) | mc pre
)
. (16)
If the post-merger first-order conditions are evaluated at the marginal costs
resulting from merger synergies, i.e., z (0) | mc post, equation 15 yields the net
merger effect:
( )
∆p nme = −A −1 z (0) | mc post ≡ g(λ). (17)
In both cases, A is evaluated at pre-merger prices and the same marginal
costs as the first-order conditions.
The net merger effects predictor can be used to compute confidence intervals.
For example, if equation 17 is parameterized by a vector of estimable
parameters λ, and ˆλ is an estimator of λ with a limiting normal distribution
√ n(ˆλ − λ) → D N(0, Σ) then √ n(g(ˆλ) − g(λ)) → D N(0, (∇g)Σ(∇g) ′ ),
provided that g is continuously differentiable at λ. Such analytic expressions
are useful for identifying factors that make confidence intervals large
and may suggest estimation strategies to reduce sampling variance. The
λ vector may include ∆mc i as well as demand parameters, reflecting the
uncertainty of synergy estimates.
If profits are a quadratic function of prices, e.g., demand is linear and
marginal costs are constant, Newton’s method converges to the post-merger
equilibrium in one step, so our one-step approximation gives the exact solution.
For other demand functions, the approximation could be refined by
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applying Newton’s method iteratively, but that would require information
about the profit functions at prices away from the observed equilibrium.
In merger simulation, the source of such “information” always has been an
arbitrary assumption about the form of demand. Without making such an
assumption, equation 17 offers the best possible approximation.
An arbitrary assumption about the form of demand can be avoided if
that form can be determined empirically, along with the elasticities at the
pre-merger equilibrium. The available data (commonly two years of scanner
data), however, normally are insufficiently informative: The range of price
variation is rather limited, and the relationship between prices and quantities
is noisy. Without better data than normally is available, distinguishing
among even large differences in pass-through rates is apt to be infeasible.
Consider the problem of empirically distinguishing among the four demand
curves in Figure 1. If prices were observed only between 10 and 12, these
four demand curves would be empirically indistinguishable unless the data
fit extraordinarily well.
3 Pass-Through Rates and Gross Merger Effects
3.1 Pass-Through Rates
We now consider how equilibrium pricing is affected by changes in costs, as
examined in the context of monopoly by Bulow and Pleiderer (1983) and
in the context of differentiated products oligopoly by Anderson, De Palma,
and Kreider (2001). We assume the effect of merger synergies on marginal
cost is invariant to output, but we do not assume that marginal cost itself is
invariant to output. In particular, merger synergies are assumed to shift the
marginal cost functions for the merged firm’s products by ∆mc = {∆mc i },
with ∆mc i independent of q i , so each post-merger cost function equals that
9

pre-merger plus q i ∆mc i .
We assume the equilibrium prices are continuous and differentiable functions
of ∆mc. Let
{ }
∂p
∂∆mc = ∂pi
∂∆mc j
(18)
be the matrix of rates at which marginal cost changes affect equilibrium
prices, with the diagonal entries being the rates at which firms pass-through
changes in their own marginal costs. Using the implicit function theorem
and differentiating the first-order conditions for post-merger equilibrium
(equation 10), it is straightforward to compute the rate at which changes in
marginal cost are passed through to prices. The pass-through-rate matrix
is
where B = {b ij } and
( )
∂p ∂z −1 ( ) ∂z
∂∆mc = − = −A −1 B, (19)
∂p ∂∆mc
b ij =
∂z i
∂∆mc j
= −w ij
∂q j
∂p i
. (20)
Hence, the impact of the marginal cost changes on equilibrium price changes
is approximated to the first order by
∆p spt ≈ −A −1 B∆mc, (21)
where the subscript “spt” denotes “synergy pass through.” The pass-throughrate
matrix (equation 19) indicates the extent to which marginal cost savings
from a merger are passed through to consumer prices in the post-merger
equilibrium and can be thought of as a predictor of the gross benefits of a
merger (under a consumer-welfare standard, which ignores profit increases).
Equation 19 is a function of both prices and the ownership structure,
W, so pass-through rates in the pre-merger equilibrium differ from those in
the post-merger equilibrium. The difference between pre- and post-merger
10

pass-through rates is most important for the cross pass-through rates of the
products of the merging firms. This difference depends on the properties
of particular demand systems, and almost anything is possible. Cross passthrough
rates may be positive pre merger but negative post merger, and
they may be substantially greater pre merger even if positive both pre and
post merger.
The W matrix incorporated in equation 21 through A and B reflects
the post-merger ownership structure, while the derivatives in equation 21 are
evaluated at pre-merger prices. Like the gross and net merger effect predictors,
the synergy effect predictor incorporates only information potentially
available at the observed pre-merger equilibrium.
The second-order conditions for Bertrand equilibrium require that the
A matrix be negative definite, and this imposes restrictions on the passthrough
matrix, −A −1 B.
For example, in an industry characterized by
single-product firms, −A −1 is positive definite and B is a diagonal matrix,
with b ii = −∂q i /∂p i along the main diagonal. This implies that own passthrough
rates are positive. And in a symmetric industry with single-product
firms, all of the b ii are the same, so B is a scalar times the identity matrix,
which implies that the pass-through matrix is positive definite.
3.2 The Relationship Between Pass-Through
Rates and Merger Effects
Adding the gross merger effect of equation 16 and the synergy effect of
equation 21 yields the net merger effect:
( )
∆p gme + ∆p spt ≈ −A −1 z (0) | mc pre + B∆mc . (22)
Because A is the matrix of derivatives with respect to prices of the vector of
first-order conditions for profit maximization, equation 22 clearly indicates
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the influence of demand second derivatives, through A, on both the gross
merger effect and the pass-through effect. The terms in the parentheses in
equation 22 include only first derivatives: z (0) | mc pre is the vector of firstorder
conditions evaluated at the pre-merger marginal costs (equation 12),
while B is the matrix of demand partial derivatives multiplied by profit
ownership shares (equation 20). Holding these two terms constant, there
is a one-to-one relationship between gross merger effects and pass-through
rates. This relationship is manifest in Figure 1 (and in Table 2 below).
It is easy to understand why the gross merger effects and pass-through
rates both depend on demand concavity. The first-order conditions characterizing
equilibrium are the first derivatives of the profit functions. The
extent to which equilibrium is displaced by a merger or marginal cost reduction
thus depends on the derivatives of the first-order conditions, and
hence on concavity of the profit function, which in this model is determined
by demand concavity.
Data relating to the abandoned WorldCom-Sprint merger can be used
to illustrate the relationship between merger effects and pass-through rates.
Shares and estimated elasticities of demand for residential long-distance service
are taken from Hausman’s (2000) submission to the Federal Communications
Commission in opposition to the merger. We assume a common
pre-merger price of $0.07 per minute. AT&T was the largest carrier with
63.4% of the domestic residential long-distance minutes, followed by World-
Com with 16.4% and Sprint with 5.0%. We place all other firms in the
residual category, “Emerging,” treating them as a single price-setting entity
in the simulations below. This treatment imparts a slight upward bias
to the simulated merger effects. Hausman’s estimated elasticity matrix is
presented in Table 1. The columns relate to prices and the rows relate to
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quantities, so the figure in the third column of the first row is the elasticity
of AT&T’s demand with respect to Sprint’s price.
Table 1: Estimated Elasticity Matrix for Residential Long Distance Carriers
AT&T WorldCom Sprint Emerging
AT&T −1.12 0.09 0.03 0.16
WorldCom 0.50 −1.33 0.06 0.23
Sprint 0.61 0.22 −1.81 0.30
Emerging 0.47 0.12 0.04 −1.33
Three different commonly used demand systems—linear, AIDS (without
income effects), and constant elasticity—are calibrated to the same premerger
equilibrium, i.e., the same prices, quantities, and elasticities (see
Crooke et al. (1999) for calibration details). Table 2 displays the resulting
merger effects as well as the marginal pass-trough rates at the post-merger
equilibrium. We suppose that all of the merger synergies accrue to the
Sprint product and examine the pass-through rates to the prices of all four
products. These pass-through rates are not approximations; the assumption
of specific demand forms makes approximation unnecessary.
Table 2: Gross Merger Effects and Pass-Through Rates for the WorldCom-
Sprint Merger
Demand Merger Effect Pass-through Rate from Sprint Cost to
Form %∆p W C+Sp AT&T WorldCom Sprint Emerging
Linear 2.3 0.007 0.001 0.502 0.008
AIDS 13.8 0.046 0.032 1.807 0.052
Isoelastic 16.4 0.000 −0.343 3.838 0.000
The striking feature of Table 2 is the difference across demand systems
in predicted gross merger effects and pass-through rates.
With isoelastic
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demand, both the merger effect and Sprint’s own pass-through rate (from
Sprint’s marginal costs to Sprint’s price) are over seven times as large as
they are with linear demand. Since all demand systems have the same
elasticities by construction, the differences across systems are due to the
different second derivatives.
4 Compensating Marginal Cost Reductions
While demand second derivatives are important determinants of both merger
and pass-through effects, Werden (1996) and Stenneck and Verboven (2001)
have shown that the marginal cost reductions necessary to keep prices constant
depend only on first derivatives, prices, and quantities. These “compensating
marginal cost reductions” can be computed by setting the term
in parentheses in equation 22 to zero, and solving for ∆mc:
∆mc comp = −B −1 z (0) | mc pre . (23)
Compensating marginal cost reductions are robust with respect to different
demand forms, in that they do not depend on the concavity of demand.
This is easily seen from the fact the matrix B and the vector z (0) contain
only first-order terms. And since prices do not change, the non-merging
firms’ first-order conditions remain at zero, so the elements of z (0) corresponding
to the non-merging firms are zero. The matrix W, and thus the
matrix B, has a block-diagonal form, with the merging products forming
a block. Because the inverse of B is also block diagonal, the compensating
marginal cost reductions depend only on the elements corresponding
to the merging products. Using Hausman’s estimated elasticities from the
WorldCom-Sprint merger, the compensating marginal cost reductions are
19% for Sprint and 13% for WorldCom, measured as a percentage of their
14

pre-merger marginal costs.
When merger synergies exactly offset the gross merger effects, the passthrough
rates can be computed by dividing the gross merger effect, ∆p gme ,
by the compensating marginal cost reductions, ∆mc comp . Thus, there is a
simple relationship between compensating marginal cost reductions, gross
merger effects, and merging product demand elasticities. This relationship
allows a useful analysis of pass-through rates that does not depend on second
derivatives of demand and hence is not dependent on its functional form.
5 Pass Through in Staples–Office Depot
As discussed by Dalkir and Warren-Boulton (2004), in 1997 the Federal
Trade Commission successfully challenged the merger of Staples and Office
Depot, the two largest office supply superstore chains in the US. In opposing
the merger, the FTC’s economic experts estimated that 85% of industrywide
marginal cost reductions had been passed through to retail prices,
while only 15% of firm-specific marginal cost reductions had been passed
through (Ashenfelter et al., 1998). The court relied on the latter estimate
in determining that synergies generated by the merger were insufficient to
prevent price increases.
As discussed by Ashenfelter et al. (2004) and Baker (1999), the FTC’s
economic experts also used panel data to estimate the price effect of changing
the number of office superstores, assuming no synergies. Public sources
report only nationwide average price increase predictions for the merger,
reflecting both cities in which the merging firms were the only office supply
superstores and cities in which there was a third superstore. Based the
reported estimates, we assume a predicted price increase of 7.5% for the
cities with just the merging firms.
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The analysis of the preceding section provides a check for the consistency
of the estimated firm-specific pass-through rate with the predicted price increase.
Assuming the merging firms were symmetric in all relevant respects,
Werden (1996) shows that the compensating marginal cost reduction relative
to pre-merger price, can be computed as
∆mc
p
= − dm
1 − d , (24)
where m is the price-marginal cost margin and d is the diversion ratio from
one superstore to another, d = ɛ ij /ɛ ii . Rearranging the result at the end of
the preceding section, the implied compensating marginal cost reductions
are given by the gross merger effect (7.5%) divided by the firm-specific passthrough
rate (15%). This yields a compensating marginal cost reduction of
50% of price for both merging firms, so equation 24 implies d = 1/(1 + 2m).
Symmetry also implies the aggregate elasticity of demand for office superstores,
ɛ, divided by the individual firm own-price elasticity, ɛ ii , equals
1 − d. Since Betrand equilibrium implies ɛ ii = −1/m, the solution for d as
a function of m implies ɛ = −2/(1 + 2m). To check for consistency, this
relationship implied by the price-increase and pass-through rate predictions
can be compared with what may have been known about margins and the
aggregate elasticity of office superstore demand.
We suspect that aggregate
demand for office supply superstores was known to be rather elastic
because there were many alternative sources for office supplies. If so, the
price-increase prediction was inconsistent with the pass-through prediction,
since ɛ < −2 implies m < 0, which surely was not the case. This conclusion,
however, depends on the assumption of Bertrand competition, and we do
not know whether this is what the FTC had in mind.
An additional check on the internal consistency of the predictions of the
FTC’s economists follows from Section 3.1. This check employs the 15%
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firm-specific pass-through rate estimated and the estimated industry-wide
pass-through rate of 85%. In a symmetric Bertrand industry, the industrywide
pass-through rate is the sum of the elements of any row in the passthrough
matrix. Assuming symmetry and that both of the estimates from
Ashenfelter et al. (1998) were correct, it is simple to compute the implied offdiagonal,
or cross, pass-through rates—those from the costs of one merging
firm to the other merging firm’s price.
In two-superstore cities, the cross pass-through rates in each row would
have to be 70%, causing the pass-through matrix not to be positive definite,
and causing the second-order conditions for Bertrand equilibrium not to be
satisfied. Another way to see this is to translate the cross pass-through rates
into slopes of best-response functions. This translation is straightforward
because the cross pass-through effect is just a response to a rival’s price
change. The slopes of the two best-response functions are just the ratio of
the cross and own pass-through rates, which is 70/15. With these slopes, the
best-response functions would not cross, and equilibrium would not exist.
Finally, even if the estimated pass-through rates were correct and accurate
in the Staples–Office Depot case, they may have been misleading,
because the merger would have caused the pass-through rates to change.
The changes in prices resulting from the merger, and the changes in ownership
that the merger bring about, both affect the pass-through rates. Postmerger
pass-through rates could not have been estimated directly, but could
have been constructed from the parameters of the firm-level profit functions.
6 Discussion
The net price effects of mergers is the touchstone for the legality of mergers
under current law in the US and many other jurisdictions, and we present a
17

igorous methodology for implementing that policy. We show that there is a
strong relationship between the gross consumer costs imposed by a merger,
i.e., the increases in consumer prices absent synergies, and the gross consumer
benefits derived from the merger, i.e., the pass through to consumer
prices of marginal cost reductions from merger synergies. Holding constant
the first-order conditions at the pre-merger equilibrium, higher-order properties
that cause larger price increases absent synergies also cause merger
synergies to be passed through at higher rates.
The gross price effects and pass-through effects of mergers can be jointly
estimated using the net merger predictor presented in equation 17. The
second derivatives of the profit (demand) function play a vital role in determining
both effects, and the estimator of the net merger effect is crucially
dependent on them. As an alternative to estimating demand second derivatives,
one can compute the compensating marginal cost reductions necessary
to offset the merger price effects. These depend only on the first-order conditions
at the pre-merger equilibrium, which in principle are observable. By
comparing likely cost reductions with these compensating marginal cost reductions,
it generally is possible to determine whether prices are likely to
rise or fall.
The foregoing is predicated on the assumption of Bertrand competition,
but similar results obtain with other Nash non-cooperative equilibria. The
conditions characterizing such equilibria are first derivatives of the profit
functions, so the displacement of equilibrium by either merger or marginal
cost reductions is determined by the concavity of the profit functions. In
other models, however, profit concavity may not be controlled by the form
of demand. Tschantz, Crooke, and Froeb (2000) show that the distribution
of costs is critical in a first- or second-price private-values auction model.
18

Generalizations of the Bertrand model may affect pass through significantly.
Froeb, Tschantz, and Werden (2002) show that adding a monopoly
retail sector downstream of the merging Bertrand competitors may change
nothing or everything, depending on the rules of the game and terms of the
contracts between the retailer and the upstream competitors. One possible
outcome is no pass through at all. We have not explored the impact of nonlinear
pricing or long-term contracts between the merging firms and ultimate
consumers, but either could make it possible for fixed-cost reductions to be
pass through, although they are not in Betrand competition. Merger policy
in both the US and Europe gives little or no weight to fixed cost-reductions
from merger synergies because they are not expected to be passed through.
19

Acknowledgments
Support for this project was provided by the Dean’s fund for faculty research.
We acknowledge useful comments from Jon Baker, Tim Brennan,
Serdar Dalkir, Joe Farrell, Gautam Gowrisankaran, P.J.J. Herings, Gregory
Leonard, John Ratcliffe, Frank Verboven, and Wes Wilson.
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